Hello, welcome to the forum.
Safecoins are actually data, and they’re stored on the network. So, to keep it simple, there are 10 coins, and each coin has an address. The addresses are 1,2,3,4,5,6,7,8,9,10. You have the ownership of coin nr. 9. So when people look in box nr. 9, they’ll see that the owner is “GkiuNBbmfghLKJm,bkhgkouyoyo”. And that’s you! So when you want to pay to me, you’ll sign a message using a “digital signature” which says: "Hi, I’m GkiuNBbmfghLKJm,bkhgkouyoyo and I want to give the ownership of this coin to CghHJGjhkjkjPJopjpRYYRkjklj. A close group of transaction managers will get your message, check the digitale signature and lookup who owns the coin at address 9. Now they see that it’s indeed you. So they’ll execute your request and change the ownership from your address to mine (the group signs that request as well). So as long you can prove to be you (have the private key to create the digital signature), you can do transactions when you have coins. But when you send your coins to someone else, it’s registered in the network that you no longer have the ownership.